The correct option is B R1={(x,y)|y=2x+1,x∈X,y∈Y}
We have
X={1,2,3,4} and Y={1,3,5,7,9}.
X×Y={(1,1),(1,3),(1,5),(1,7),(1,9),(2,1),(2,3),(2,5),
(2,7),(2,9),(3,1),(3,3),(3,5),(3,7),(3,9),(4,1),(4,3),(4,5),(4,7),(4,9)}
Let's take option A,
R1={(x,y)|y=2x+1,x∈X,y∈Y}
R1={(1,3),(2,5),(3,7),(4,9)}
Since, R1⊆X×Y
So, R1 is a relation from X to Y
Clearly, R2 is not a relation from X to Y as (5,5)∉X×Y
Similarly, R3 is not a relation from X to Y as (5,7)∉X×Y
In the same manner, R4 is also not a relation from X to Y as (7,9)∉X×Y